We consider a nonlinear elliptic equation driven by the sum of a $p$--Laplacian and a $q$--Laplacian where $1<q\leq2\leq p<\infty$ with a $(p-1)$--superlinear Carath\'eodory reaction term which doesn't satisfy the usual Ambrosetti--Rabinowitz condition. Using variational methods based on critical point theory together with techniques from Morse theory, we show that the problem has at leat three nontrivial solutions; among them one is positive and one is negative.

Wang’s multiplicity result for superlinear $(p,q)$–equations without the Ambrosetti–Rabinowitz condition

MUGNAI, Dimitri;
2014

Abstract

We consider a nonlinear elliptic equation driven by the sum of a $p$--Laplacian and a $q$--Laplacian where $1
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1232503
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